Comb Tensor Networks vs. Matrix Product States: Enhanced Efficiency in High-Dimensional Spaces

TL;DR

This paper shows that comb tensor networks can outperform traditional matrix product states in efficiently modeling high-dimensional continuous data, reducing computational costs while preserving accuracy.

Contribution

It introduces the comb tensor network architecture as a more efficient alternative to MPS for high-dimensional data modeling.

Findings

Comb tensor networks outperform MPS in contraction efficiency beyond certain data dimensions.

Transitioning to comb tensor networks reduces computational overhead.

The approach maintains accuracy in modeling high-dimensional data.

Abstract

Modern approaches to generative modeling of continuous data using tensor networks incorporate compression layers to capture the most meaningful features of high-dimensional inputs. These methods, however, rely on traditional Matrix Product States (MPS) architectures. Here, we demonstrate that beyond a certain threshold in data and bond dimensions, a comb-shaped tensor network architecture can yield more efficient contractions than a standard MPS. This finding suggests that for continuous and high-dimensional data distributions, transitioning from MPS to a comb tensor network representation can substantially reduce computational overhead while maintaining accuracy.